Rule 30

# References

Equation
Rule 30 (page 27): Mod[p + q + r + q r, 2]
http://www.wolframscience.com/nksonline/page-869b-text?firstview=1

Wolframs notes on rule 30
http://www.wolframscience.com/nksonline/page-27-text

p and q are the neighbors on the left and r and s are the neighbors on the right. The cell being updated doesn't participate.

Mod (Maths function)

A form of arithmetic dealing with integers in which all numbers having the same remainder when divided by a whole number are considered equivalent: Clocks use modular arithmetic with modulus 12, so 4 hours after 9 o'clock is 1 o'clock. http://www.answers.com/topic/modular-arithmetic

More generally, modular arithmetic also has application in disciplines such as law (see e.g., apportionment), economics, (see e.g., game theory) and other areas of the social sciences, where proportional division and allocation of resources plays a central part of the analysis.

In cryptography, modular arithmetic directly underpins public key systems such as RSA and Diffie-Hellman, as well as providing finite fields which underlie elliptic curves, and is used in and a variety of symmetric key algorithms including AES, IDEA, and RC4.

Special functions
Rule 30 and zeta function
http://www.stephenwolfram.com/publications/talks/specialfunctions/